Matrix generalised Kummer relation

  • José A. Díaz-García Department of Statistics and Computation, Universidad Autonoma Agraria Antonio Narro, 25315 Buenavista, Saltillo, Coahuila, Mexico
  • Francisco J. Caro-Lopera Department of Basic Sciences, Universidad de Medellín, Carrera 87 No.30-65, of. 5-103, Medellín, Colombia
Keywords: Hypergeometric function, Matrix Kummer relations, Zonal polynomials


An extension of the well known matrix Kummer relation of Herz (1955) is proposed in this paper by assuming a general model which admits a Taylor expansion. Under certain conditions of the involved parameters, the addressed generalisation can be used for deriving efficiently computable matrix variate densities based on non Gaussian models, avoiding some open problems of the literature in the context of shape theory and other related fields.


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